Always, sometimes, never questions are often very difficult for my students. I designed this task to help all of my students to be successful, while still attaining an appropriate level of rigor. By helping students to structure their responses, this exercise helps the students to recall and compare the different features of the special quadrilaterals. By having the students work together in pairs, the students are asked to communicate, to reason, and to justify.

If students are struggling with the task, they usually benefit from using their Family Tree of Quadrilaterals as a resource. I find that students who were able to internalize this model have less difficulty with the task.

Always...Sometimes...Never...Ugh

Rigor: Always...Sometimes...Never...Ugh

Problem Solving with Quadrilaterals, Part 3

Problem Solving with Quadrilaterals, Part 3

Unit 8: Quadrilaterals
Lesson 5 of 5

Objective: Students will be able to reason about the properties of quadrilaterals and use them to solve measurement problems.

Today is another work day. Before we return to the Problem Sets, though, we'll compelte a warmup activity. As my students enter the room, I give each pair a set of twelve Always, Sometimes, Never cards that I cut out prior to the class. Students also receive the accompanying sheets with titles “Always True,” “Sometimes True,” and “Never True.” Each pair of students is also provided with a glue stick.

Pairs are instructed to discuss and to decide on which of the three sheets the cards should go, then glue the cards in place. If a statement is always true, the students are asked to explain why it is true on the sheet. Their answers can be given in the form of a statement or a diagram – whatever type of justification they choose. If a statement is sometimes true, they are asked to provide an example of when the statement is true and when it is false. If a statement is never true, they are asked to explain why it is never true and to amend the statement so that it would always be true.

When the pairs have completed their work, I ask them to compare their answers to the answers given by the other pair at their table. When everyone has had a chance to discuss their answers, I ask if there are any cards on which the tables disagree; if so, we discuss those cards as a class.

Resources

After we discuss the Warmup task, I my students to continue to work on Quadrilateral Practice 2. When students finish this problem set, I hand out Quadrilateral Practice 3. This set contains no diagrams, so that students must draw their own diagrams in order to solve the problems. This fact makes these problems very challenging for some of my students. I am ready to work with them to help them practice creating diagrams.

As I have over the last two days, I circulate around the room. I focus on groups or individuals who might be struggling. When students ask for help, I ask a series of questions:

- Have you filled in all of the information you know on your diagram?

- What do you know about a _______________?

- Have you indicated that on your diagram?

I find that using questioning to focus students attention on creating a model and thinking about properties helps most students reach a point where they can say, “Oh, yeah. Now I know how to do it.”

Teacher's Note: At the bottom of Quadrilateral Practice 3 there is a challenge question in which I ask my students to investigate the figure that is formed by joining the midpoints of the four sides of a quadrilateral. This question will be a focus of our investigation in the next lesson. will lead into the topic for the next lesson (Midsegments and Medians).

Resources

We'll complete today's lesson with a group problem, which I will write on the board:

Parallelogram ABCD has AB = 20 and BC = 20.

What can you tell me about this parallelogram?

I ask the students to work in their groups for approximately 3 minutes, and, while the students work, I draw the diagram for this problem on the board. I then ask each group to share with the class one piece of information about ABCD. As the groups provide information, I fill their information in on the diagram and we discuss each group’s input.

For homework, I ask that everyone work on Quadrilateral Practice 3. For those who are just beginning this problem set, I suggest that they focus on drawing the diagrams and filling in the given information for several problems in order to practice this skill.